Kinda think you're missing a fundamental principle of science in general and of biology in particular:
https://en.wikipedia.org/wiki/Folk_taxonomy
The point of the standard biological definitions for the sexes is that they apply to
ALL anisogamous species,
NO exceptions. Something that evolutionary biologist (a practicing one for those keeping score, at least if they're able to count ...) and transwoman Joan Roughgarden emphasized in Paul Griffiths' paper:
https://philarchive.org/rec/GRIWAB-2
https://en.wikipedia.org/wiki/Joan_Roughgarden
But I kind think there's a "mistranslation" in "gonochorism":
https://en.wikipedia.org/wiki/Gonochorism
See a bit of etymology:
https://www.uvm.edu/~jbailly/courses/clas22/lessons/GreekLesson11.html
There is absolutely nothing in either of those that justifies the previous claim from Wikipedia that "each individual organism is either male or female". Which very much depends on how one defines "male" and "female" in the first place. All they're saying, in effect, is that all sexed individual organisms -- i.e., those with a sex -- are either male or female.
ETA: You might also note that ovotestis, while rare but not unheard of in humans, are found in mice and moles:
https://en.wikipedia.org/wiki/Ovotestis
So mice and moles and some humans aren't "organized around producing either type of gamete". Though maybe moot in the case of mice and moles -- maybe they can subsequently develop into either like clownfish.
But there goes your "usefully applied" ...